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AN EFFECTIVE ALGORITHM FOR COMPUTING FRACTIONAL DERIVATIVES AND APPLICATION TO FRACTIONAL DIFFERENTIAL EQUATIONS

期刊: INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2021; 18 (4)

In recent years, fractional differential equations have been extensively applied to model various complex dynamic systems. The studies on highly accur......

A DEEP LEARNING GALERKIN METHOD FOR THE SECOND-ORDER LINEAR ELLIPTIC EQUATIONS

期刊: INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2021; 18 (4)

In this paper we propose a Deep Learning Galerkin Method (DGM) based on the deep neural network learning algorithm to approximate the general second-o......

STABILIZED INVARIANT ENERGY QUADRATIZATION (S-IEQ) METHOD FOR THE MOLECULAR BEAM EPITAXIAL MODEL WITHOUT SLOPE SECTION

期刊: INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2021; 18 (5)

The design of numerical approaches for the molecular beam epitaxy models has always been a hot issue in numerical analysis, in which one of the main c......

GLOBAL WELL-POSEDNESS FOR NAVIER-STOKES-DARCY EQUATIONS WITH THE FREE INTERFACE

期刊: INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2021; 18 (5)

In this paper, the Navier-Stokes-Darcy equations with the free interface are considered, which model the movement of the sea and the sand in the seafl......

LOCKING-FREE CG-TYPE FINITE ELEMENT SOLVERS FOR LINEAR ELASTICITY ON SIMPLICIAL MESHES

期刊: INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2021; 18 (5)

This paper presents numerical methods for solving linear elasticity on simplicial meshes based on enrichment of Lagrangian bilinear/trilinear finite e......

A COMPACT FINITE DIFFERENCE SCHEME FOR THE FOURTH-ORDER TIME MULTI-TERM FRACTIONAL SUB-DIFFUSION EQUATIONS WITH THE FIRST DIRICHLET BOUNDARY CONDITIONS

期刊: INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2021; 18 (1)

In this paper, a finite difference scheme is established for solving the fourth-order time multi-term fractional sub-diffusion equations with the firs......

LOCALLY CONSERVATIVE SERENDIPITY FINITE ELEMENT SOLUTIONS FOR ELLIPTIC EQUATIONS

期刊: INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2021; 18 (1)

In this paper, we post-process an eight-nodes-serendipity finite element solution for elliptic equations. In the post-processing procedure, we first c......

WELL-POSEDNESS AND THE MULTISCALE ALGORITHM FOR HETEROGENEOUS SCATTERING OF MAXWELL'S EQUATIONS IN DISPERSIVE MEDIA

期刊: INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2021; 18 (2)

This paper discusses the well-posedness and the multiscale algorithm for the heterogeneous scattering of Maxwell's equations in dispersive media with ......

FINITE VOLUME ELEMENT METHOD FOR PREDICTING ELECTROSTATICS OF A BIOMOLECULE IMMERSED IN AN IONIC SOLVENT

期刊: INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2021; 18 (2)

Poisson-Boltzmann equation (PBE) is a classic implicit continuum model to predict the electrostatic potentials of a solvated biomolecule. In this pape......

NUMERICAL SIMULATIONS FOR SHALLOW WATER FLOWS OVER ERODIBLE BEDS BY CENTRAL DG METHODS

期刊: INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2021; 18 (2)

In this paper, we investigate the shallow water flows over erodible beds by using a fully coupled mathematical model in two-dimensional space. This mo......

A POSITIVITY-PRESERVING AND CONVERGENT NUMERICAL SCHEME FOR THE BINARY FLUID-SURFACTANT SYSTEM

期刊: INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2021; 18 (3)

In this paper, we develop a first order (in time) numerical scheme for the binary fluid surfactant phase field model. The free energy contains a doubl......

A STOCHASTIC GRADIENT DESCENT METHOD FOR THE DESIGN OF OPTIMAL RANDOM INTERFACE IN THIN-FILM SOLAR CELLS

期刊: INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2021; 18 (3)

Random rough texture design can be used to find the optimal design of random surfaces in thin film solar cells to increase their absorbing efficiency.......

STABILITY OF HIGH ORDER FINITE DIFFERENCE SCHEMES WITH IMPLICIT-EXPLICIT TIME-MARCHING FOR CONVECTION-DIFFUSION AND CONVECTION-DISPERSION EQUATIONS

期刊: INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2021; 18 (3)

The main purpose of this paper is to analyze the stability of the implicit-explicit (IMEX) time-marching methods coupled with high order finite differ......

ERROR ESTIMATES FOR THE LAPLACE INTERPOLATION ON CONVEX POLYGONS

期刊: INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2021; 18 (3)

In the natural element method (NEM), the Laplace interpolation error estimate on convex planar polygons is proved in this study. The proof is based on......

A STABILIZER FREE WEAK GALERKIN FINITE ELEMENT METHOD FOR GENERAL SECOND-ORDER ELLIPTIC PROBLEM

期刊: INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2021; 18 (3)

This paper proposes a stabilizer free weak Galerkin (SFWG) finite element method for the convection-diffusion-reaction equation in the diffusion-domin......

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